Decentralized stabilization for structurally balanced networks with similar nodes

This paper studies the stabilization problem of complex dynamical networks with nonlinear similar nodes and arbitrary finite communication delays, while the networks are structural balance. For the considered networks, the information flow is undirected or directed, and only locally delayed information can be used for each node. We derive that stabilization of structurally balanced networks can be realized by designing decentralized controllers, when the associated assumptions are true. Furthermore, the proposed stabilization schemes are also useful to the structurally balanced networks without communication delays. Finally, the simulations are presented to show the effectiveness of the method in this paper.